The present invention is directed to a new permeameter-porosimeter (hereinafter referred to as xe2x80x9cpermeameterxe2x80x9d) to measure the permeability and porosity of porous materials in normal and lateral (i.e. perpendicular to the normal) directions. The permeability of woven or non-woven, sheet or plate porous materials such as paper, cloth, plastic foam, fritted glass, metal-wool, powder metal, etc. can be measured with the new permeameter. The permeameter of the present invention is well suited for measuring the permeability of friction materials for wet clutch applications; however, it can be applied to any porous material which has three-dimensional structural integrity. The new permeameter is capable of compressing a sample mechanically and taking permeability measurements on the compressed sample. The permeameter also allows measurements at elevated temperatures up to 150xc2x0 C. The permeameter measures permeability, porosity, pore size distribution, average pore size and number of pores per unit area.
The importance of permeability on the performance of friction materials has been demonstrated in the mathematical models of clutch engagement. However, there is little experimental information on the permeability of friction materials partly due to the absence of a permeameter which can take accurate measurements in normal as well as lateral directions.
The permeability of friction material has a significant impact on torque response as the permeability affects the initial coefficient of friction.
In the past, an oil absorption test has been used as an indirect measure of the permeability and porosity of friction materials. However, the oil absorption test has certain shortcomings which are overcome by the permeameter of the present invention.
The permeameter of the present invention includes three units: 1) sample compartment with compression capability; 2) fluid chamber containing permeant and having a pressuring piston and a temperature control; and, 3) fluid storage tanks and closed loop transport lines to fill the fluid chamber. Permeant fluid can be gas or liquid depending on the test method. The permeant fluid is forced through the sample under pressure. Measurements of load, fluid displacement, flow time, sample thickness and sample weight before and after the test are recorded and used in the calculations of permeability, porosity, pore size distribution, average pore size and number of pores per unit area.
Normal permeability and lateral permeability are measured separately. The normal permeability measurement requires a disk shaped sample and the lateral permeability measurement requires a ring shaped sample. Both samples can be punched out in a single die cut operation where the disk sample is the center slug of the ring sample. In the normal permeability test, the penetrating fluid is forced through the disk sample along the thickness from one flat side to the other. In the lateral permeability test, the fluid is forced through the ring sample along the annulus from inner diameter to the outer diameter.
Sometimes it is necessary to measure the permeability of materials (especially of the highly compressible ones) when they are under compression. Compression changes the shape and the size of the pores, thereby effecting the permeability. For example, a paper based gasket material functions under a compression to prevent oil leakage. It is important to know the optimum compression needed for an effective sealing since under-compression causes leakage and over-compression reduces the life of gasket. The permeameter of the present invention has the ability to mechanically compress the sample and take permeability measurements on the compressed sample.
A commercially available universal test machine with calibrated force and displacement controls my be used to actuate the piston of the permeameter. The permeameter of the present invention may be used to measure the lateral permeability of a wide range of finished friction plates up to 190 mm diameter.
A Reynolds number check indicates that the flow is laminar during a liquid permeability test. Hence, Darcy""s formula is applicable to calculate the permeability constant. Furthermore, it is also assumed that all the pores are cylindrical and of same size. In reality, the pores have random shape and size. However, the uniform pore assumption lets us to calculate an equivalent mean pore diameter, and an equivalent number of pores for the tested samples.
The normal permeability is calculated using the following formula:                               k          z                =                              Q            ⁢                          xe2x80x83                        ⁢            η            ⁢                          xe2x80x83                        ⁢            l                                Δ            ⁢                          xe2x80x83                        ⁢            P            ⁢                          xe2x80x83                        ⁢            A                                              (        1        )            
kz is the normal permeability (m2)
Q is flow rate (m3/s)
xcex7 is the absolute viscosity of the fluid (Ns/m2)
l is the distance fluid flow through the sample (m)
xcex94P is the pressure difference between fluid inlet and outlet (Pa)
A is the sample area through which fluid flows (m2)
The lateral permeability is calculated using the following formula:                               k          r                =                              Q            ⁢                          xe2x80x83                        ⁢            η            ⁢                          xe2x80x83                        ⁢                          ln              ⁡                              (                                                      r                    0                                                        r                    i                                                  )                                                          2            ⁢            π            ⁢                          xe2x80x83                        ⁢            t            ⁢                          xe2x80x83                        ⁢            Δ            ⁢                          xe2x80x83                        ⁢            P                                              (        2        )            
where kr is the lateral permeability, ro and rl outer and inner diameter of ring sample, and t is the thickness of sample.
The ratio of the volume of the liquid permeant absorbed by the sample to the geometric volume of the sample gives the percent porosity. The percent porosity is calculated from the weight difference of the sample before and after the permeability test using the following formula:                               φ          p                =                                                            W                A                            -                              W                B                                                    ρ              ⁢                              xe2x80x83                            ⁢              V                                ⁢          100                                    (        3        )            
where xcfx86p is the percent porosity, WA and WB are the sample weight after and before the test, xcfx81 is the density of the fluid, V is the geometric volume of the sample.
The average pore size is determined assuming that the pores are cylindrical, straight, and of equal diameter. Flow through a capillary pore of diameter dp and length l is given by the following formula:                     q        =                              π            ⁢                          xe2x80x83                        ⁢                          d              p              4                        ⁢            Δ            ⁢                          xe2x80x83                        ⁢            P                                128            ⁢            η            ⁢                          xe2x80x83                        ⁢            l                                              (        4        )            
Total flow through the sample (Q) is found by multiplying the flow through one pore (q) by the number of pores (N):
Q=Nqxe2x80x83xe2x80x83(5)
The total number of pores (N) is obtained by dividing the total pore volume (Vp) to a single pore volume (vp):                     N        =                              V            p                                v            p                                              (        6        )            
The total pore volume (Vp) is found by multiplying the volume of the sample (V) with the percent porosity (xcfx86p)                               V          p                =                  V          ⁢                                    φ              p                        100                                              (        7        )            
The individual pore volume is                               v          p                =                              π            ⁢                          xe2x80x83                        ⁢                          d              p              2                        ⁢            l                    4                                    (        8        )            
Where (dp) is the pore diameter and (l) is the pore length. In normal permeability, l is equal to the thickness of the disk sample. In lateral permeability, l is equal to the width of the annulus of the ring sample. The mean pore diameter (dp) is calculated by replacing equations 4, 6, 7, and 8 in 5 and extracting dp                              d          p                =                              (                                          3200                ⁢                                  xe2x80x83                                ⁢                                  l                  2                                ⁢                Q                ⁢                                  xe2x80x83                                ⁢                η                                            Δ                ⁢                                  xe2x80x83                                ⁢                P                ⁢                                  xe2x80x83                                ⁢                V                ⁢                                  xe2x80x83                                ⁢                                  φ                  p                                                      )                                1            /            2                                              (        9        )            
The number of pores per unit sample area (Nper mm2) is given in terms of porosity (xcfx86p) and mean pore diameter (dp) as follows:                               N                      p            ⁢                          xe2x80x83                        ⁢            e            ⁢                          xe2x80x83                        ⁢            r            ⁢                          xe2x80x83                        ⁢                          mm              2                                      =                              φ            p                                25            ⁢            π            ⁢                          xe2x80x83                        ⁢                          d              p              2                                                          (        10        )            
where dp is in mm.
Pore size distribution is obtained using air as the permeant. The flow rate of air is measured under a ramping air pressure on a dry sample. The dry sample is removed from the permeameter and saturated with a low surface tension wicking fluid until the sample is completely wet. Then, the air flow rate measurement is repeated on the wet sample under the ramping pressure. The flow rate difference between the dry sample and the wet sample at each pressure interval yields information on the pore size distribution.
Fluids of different viscosities can be used in the measurements in order to have enough retention time for accurate measurements. For example, while oil is used for the normal permeability, water can be used for the lateral permeability measurement. Permeability and porosity calculations require the measurements of flow rate and volume of retained fluid, respectively. Permeability (k) and porosity (xcfx86) are independent parameters since the flow rate and the retained fluid volume are measured independently. On the other hand, pore size (d) and number of pores (N) are coupled parameters and not independent from permeability and porosity.